1. Field of the Invention
The present invention relates to methods and systems for simulating a financial parameter and, more particularly, to methods and systems for simulating securities valuations and for assisting a user in making an investment decision.
2. Description of Related Art
The introduction of quantitative analysis methods into the financial services arena has become attractive to market participants. However, all but the largest users are forced to use simple techniques, because of prohibitively expensive software and hardware. In addition to cost, investors must learn how to install, use, and maintain proprietary software and frequently must purchase different software for different investment or risk management tasks.
At present, theoretical pricing models are used as market benchmarks. Traders use the models to obtain implied volatilities from current market prices. They may combine implied parameters with historical analysis. Then they use the model with these parameters to construct hedges with respect to various parameters and to predict option price movements as the stock prices move in the short run. The models are also used to consistently price new options with respect to actively traded ones. This can be done quickly only using analytical methods, but the analytical methods are very restrictive and even outright wrong in their assumptions about how the markets work. Numerical methods are much more flexible, but are much slower, particularly when sensitivities and multiple scenarios must be evaluated.
Monte Carlo simulation is a technique for estimating the solution of a numerical mathematical problem by means of an artificial sampling experiment. This is an established numerical method for the valuation of derivative securities. Its major strength is flexibility, and it may be applied to almost any problem, including history-dependent claims or empirically characterized security processes.
The major disadvantage of Monte Carlo simulation is speed, as the accuracy of the method improves as the square root of the number of independent samples generated in a simulation. However, because of sample independence, the method is highly parallel and is thus ideally suited for implementation with scalable parallel-processing architectures. The use of MPP permits a speed increase by a factor up to the number of processors.
The Monte Carlo approach introduced by Boyle (J. Fin. Econ. 4, 323-38, 1977) relies on direct stochastic integration of the underlying Langevin equation. Given a security price at a first time, a new price for a subsequent second time is generated at random according to the stochastic process of the security. Results are obtained by averaging over a large number of realizations of the process.
High-performance computing and communications (HPCC), and, in particular, cooperative, distributed, and parallel computing, are expected to play an increasingly important role in trading, financial engineering, and all aspects of investment and commercial banking. The convergence of a number of factors are at present, and are anticipated to continue, causing significant changes in the way in which financial transactions are implemented. Such factors include:                Increased volatility due to globalization of financial markets;        Global distribution of data sources;        Increased complexity of derivatives and other risk management vehicles;        Increased demand for real-time investment and asset allocation decision support;        Increased volume of raw data and need to process large databases;        Increased volume on the retail side of the spectrum, mainly due to on-line technologies (e.g., the Internet and the World Wide Web).        
High-performance computing technologies are becoming indispensable in the application domains such as:                Derivative valuation, particularly over-the-counter products;        Portfolio optimization and asset allocation;        Hedging of portfolios in real time;        Arbitrage trading;        Risk analysis simulations.        
Traditionally, these applications supported the wholesale end of the financial services spectrum and the supply side. It is believed that there is opportunity for HPCC being created by the emergence of global computer networks as a new delivery channel and economic force. For example, the Internet is creating a shift among financial services providers towards the retail end of the spectrum. At the same time, there is increased demand on the buy side, particularly among corporate treasurers, for more structured and more complex financial instruments to manage risk with more flexibility.
This demand is going to grow with the trend towards globalization, which will be reflected in increased short-term volatility and risk exposure for all market participants. Investors at all levels of endowment are becoming more self-reliant for investment decisions and more comfortable with technology. It is believed that this trend will be reinforced by the wealth of information offered to the public as well as value-added networks. Finally, there is increased pressure from regulators to enact sophisticated risk management strategies for institutional investors, given well-publicized recent events involving financial catastrophes. It is believed that these factors will contribute to an increased demand for on-line services in two areas:                Resources for risk management support;        Resources for investment decision support.It is believed that these trends will lead to pervasive deployment of scalable high-performance architectures to support market demands.        